Combination & Permutation Calculator (nCr & nPr)
Free nCr and nPr calculator. Find combinations (order doesn't matter) and permutations (order matters) with step-by-step explanation.
nCr & nPr Calculator
(order doesn't matter)
(order matters)
Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
1. Combinations vs Permutations
Both combinations and permutations count the number of ways to select items from a group. The key difference is whether order matters.
2. Combinations (nCr) — Order Does NOT Matter
Use when the order of selection is irrelevant. Formula: nCr = n! ÷ (r! × (n−r)!)
Example: How many ways to choose 3 students from a class of 10 to form a committee? nCr = 10!/(3! × 7!) = 120 ways.
3. Permutations (nPr) — Order DOES Matter
Use when the order of selection matters (first place, second place, etc.). Formula: nPr = n! ÷ (n−r)!
Example: How many ways can 3 students from a class of 10 be ranked 1st, 2nd, 3rd? nPr = 10!/7! = 720 ways.
4. Quick Comparison
- Pizza toppings (order doesn't matter): use Combinations.
- Race finishing positions (order matters): use Permutations.
- Choosing a 4-digit PIN (order matters): use Permutations.
- Selecting a 5-card poker hand (order doesn't matter): use Combinations.
See also: Factorial Calculator | Probability Calculator | Probability Basics